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Obtaining accurate photometric redshift estimations is an important aspect of cosmology, remaining a prerequisite of many analyses. In creating novel methods to produce redshift estimations, there has been a shift towards using machine learning techniques. However, there has not been as much of a focus on how well different machine learning methods scale or perform with the ever-increasing amounts of data being produced. Here, we introduce a benchmark designed to analyse the performance and scalability of different supervised machine learning methods for photometric redshift estimation. Making use of the Sloan Digital Sky Survey (SDSS - DR12) dataset, we analysed a variety of the most used machine learning algorithms. By scaling the number of galaxies used to train and test the algorithms up to one million, we obtained several metrics demonstrating the algorithms performance and scalability for this task. Furthermore, by introducing a new optimisation method, time-considered optimisation, we were able to demonstrate how a small concession of error can allow for a great improvement in efficiency. From the algorithms tested we found that the Random Forest performed best in terms of error with a mean squared error, MSE = 0.0042; however, as other algorithms such as Boosted Decision Trees and k-Nearest Neighbours performed incredibly similarly, we used our benchmarks to demonstrate how different algorithms could be superior in different scenarios. We believe benchmarks such as this will become even more vital with upcoming surveys, such as LSST, which will capture billions of galaxies requiring photometric redshifts.
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Knowing the redshift of galaxies is one of the first requirements of many cosmological experiments, and as its impossible to perform spectroscopy for every galaxy being observed, photometric redshift (photo-z) estimations are still of particular interest. Here, we investigate different deep learning methods for obtaining photo-z estimates directly from images, comparing these with traditional machine learning algorithms which make use of magnitudes retrieved through photometry. As well as testing a convolutional neural network (CNN) and inception-module CNN, we introduce a novel mixed-input model which allows for both images and magnitude data to be used in the same model as a way of further improving the estimated redshifts. We also perform benchmarking as a way of demonstrating the performance and scalability of the different algorithms. The data used in the study comes entirely from the Sloan Digital Sky Survey (SDSS) from which 1 million galaxies were used, each having 5-filter (ugriz) images with complete photometry and a spectroscopic redshift which was taken as the ground truth. The mixed-input inception CNN achieved a mean squared error (MSE)=0.009, which was a significant improvement (30%) over the traditional Random Forest (RF), and the model performed even better at lower redshifts achieving a MSE=0.0007 (a 50% improvement over the RF) in the range of z<0.3. This method could be hugely beneficial to upcoming surveys such as the Vera C. Rubin Observatorys Legacy Survey of Space and Time (LSST) which will require vast numbers of photo-z estimates produced as quickly and accurately as possible.
We investigate star-galaxy classification for astronomical surveys in the context of four methods enabling the interpretation of black-box machine learning systems. The first is outputting and exploring the decision boundaries as given by decision tree based methods, which enables the visualization of the classification categories. Secondly, we investigate how the Mutual Information based Transductive Feature Selection (MINT) algorithm can be used to perform feature pre-selection. If one would like to provide only a small number of input features to a machine learning classification algorithm, feature pre-selection provides a method to determine which of the many possible input properties should be selected. Third is the use of the tree-interpreter package to enable popular decision tree based ensemble methods to be opened, visualized, and understood. This is done by additional analysis of the tree based model, determining not only which features are important to the model, but how important a feature is for a particular classification given its value. Lastly, we use decision boundaries from the model to revise an already existing method of classification, essentially asking the tree based method where decision boundaries are best placed and defining a new classification method. We showcase these techniques by applying them to the problem of star-galaxy separation using data from the Sloan Digital Sky Survey (hereafter SDSS). We use the output of MINT and the ensemble methods to demonstrate how more complex decision boundaries improve star-galaxy classification accuracy over the standard SDSS frames approach (reducing misclassifications by up to $approx33%$). We then show how tree-interpreter can be used to explore how relevant each photometric feature is when making a classification on an object by object basis.
Aims: We present a custom support vector machine classification package for photometric redshift estimation, including comparisons with other methods. We also explore the efficacy of including galaxy shape information in redshift estimation. Support vector machines, a type of machine learning, utilize optimization theory and supervised learning algorithms to construct predictive models based on the information content of data in a way that can treat different input features symmetrically. Methods: The custom support vector machine package we have developed is designated SPIDERz and made available to the community. As test data for evaluating performance and comparison with other methods, we apply SPIDERz to four distinct data sets: 1) the publicly available portion of the PHAT-1 catalog based on the GOODS-N field with spectroscopic redshifts in the range $z < 3.6$, 2) 14365 galaxies from the COSMOS bright survey with photometric band magnitudes, morphology, and spectroscopic redshifts inside $z < 1.4$, 3) 3048 galaxies from the overlap of COSMOS photometry and morphology with 3D-HST spectroscopy extending to $z < 3.9$, and 4) 2612 galaxies with five-band photometric magnitudes and morphology from the All-wavelength Extended Groth Strip International Survey and $z < 1.57$. Results: We find that SPIDER-z achieves results competitive with other empirical packages on the PHAT-1 data, and performs quite well in estimating redshifts with the COSMOS and AEGIS data, including in the cases of a large redshift range ($0 < z < 3.9$). We also determine from analyses with both the COSMOS and AEGIS data that the inclusion of morphological information does not have a statistically significant benefit for photometric redshift estimation with the techniques employed here.
We present a Bayesian approach to the redshift classification of emission-line galaxies when only a single emission line is detected spectroscopically. We consider the case of surveys for high-redshift Lyman-alpha-emitting galaxies (LAEs), which have traditionally been classified via an inferred rest-frame equivalent width (EW) greater than 20 angstrom. Our Bayesian method relies on known prior probabilities in measured emission-line luminosity functions and equivalent width distributions for the galaxy populations, and returns the probability that an object in question is an LAE given the characteristics observed. This approach will be directly relevant for the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), which seeks to classify ~10^6 emission-line galaxies into LAEs and low-redshift [O II] emitters. For a simulated HETDEX catalog with realistic measurement noise, our Bayesian method recovers 86% of LAEs missed by the traditional EW > 20 angstrom cutoff over 2 < z < 3, outperforming the EW cut in both contamination and incompleteness. This is due to the methods ability to trade off between the two types of binary classification error by adjusting the stringency of the probability requirement for classifying an observed object as an LAE. In our simulations of HETDEX, this method reduces the uncertainty in cosmological distance measurements by 14% with respect to the EW cut, equivalent to recovering 29% more cosmological information. Rather than using binary object labels, this method enables the use of classification probabilities in large-scale structure analyses. It can be applied to narrowband emission-line surveys as well as upcoming large spectroscopic surveys including Euclid and WFIRST.
Star Formation Rates or SFRs are crucial to constrain theories of galaxy formation and evolution. SFRs are usually estimated via spectroscopic observations requiring large amounts of telescope time. We explore an alternative approach based on the photometric estimation of global SFRs for large samples of galaxies, by using methods such as automatic parameter space optimisation, and supervised Machine Learning models. We demonstrate that, with such approach, accurate multi-band photometry allows to estimate reliable SFRs. We also investigate how the use of photometric rather than spectroscopic redshifts, affects the accuracy of derived global SFRs. Finally, we provide a publicly available catalogue of SFRs for more than 27 million galaxies extracted from the Sloan Digital Sky survey Data Release 7. The catalogue is available through the Vizier facility at the following link ftp://cdsarc.u-strasbg.fr/pub/cats/J/MNRAS/486/1377.
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